MCMC with Delayed Acceptance using a Surrogate Model with an Application to Cardiovascular Fluid Dynamics

Paun, L. M., Colebank, M., Qureshi, M. U., Olufsen, M., Hill, N. and Husmeier, D. (2019) MCMC with Delayed Acceptance using a Surrogate Model with an Application to Cardiovascular Fluid Dynamics. In: International Conference on Statistics: Theory and Applications (ICSTA’19), Lisbon, Portugal, 13-14 Aug 2019, p. 28. ISBN 9781927877647 (doi:10.11159/icsta19.28)

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Abstract

Parameter estimation and uncertainty quantification in physiological modelling is a vital step towards personalised medicine. Current state-of-the-art in this research area performs parameter optimisation, with very limited uncertainty quantification. This paper demonstrates the advantage of novel sampling methods, applied on a complex biological PDE system of the pulmonary circulation. The aim is to find an efficient and accurate method for the inference and uncertainty quantification of unknown parameters, relevant for disease diagnosis (pulmonary hypertension) from limited and noisy blood pressure data. The data likelihood is expensive to evaluate as it requires solving numerically a system of PDEs. Therefore, having a model that best trades off accuracy and computational efficiency is of uppermost importance. In this study, we employ fast Bayesian methods, namely MCMC algorithms coupled with emulation using Gaussian Processes, to achieve a computational speed-up. We compare the Delayed Rejection Adaptive Metropolis algorithm in a History Matching framework to the delayed acceptance Adaptive Metropolis algorithm. The first algorithm draws samples from the approximate posterior distribution, while the latter is guaranteed to generate samples from the exact posterior distribution asymptotically. In this paper we propose and derive the n-steps ahead delayed acceptance Metropolis-Hastings algorithm, which is a generalisation of the classical 1-step ahead delayed acceptance Metropolis-Hastings. We show the superiority of the n-steps ahead algorithm over the 1-step ahead method.

Item Type:Conference Proceedings
Additional Information:Dirk Husmeier is supported by a grant from the Royal Society of Edinburgh, award number 62335.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Paun, Luiza and Hill, Professor Nicholas and Husmeier, Professor Dirk
Authors: Paun, L. M., Colebank, M., Qureshi, M. U., Olufsen, M., Hill, N., and Husmeier, D.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
College of Science and Engineering > School of Mathematics and Statistics > Statistics
ISSN:2562-7767
ISBN:9781927877647
Copyright Holders:Copyright © 2019 International ASET Inc.
First Published:First published in Proceedings of the International Conference on Statistics: Theory and Applications (ICSTA’19): 28
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
694461EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - MATHEMATICS